Rotational Angular Momentum Quantum Number Research Articles

Structure and dynamics of HD+ in the vicinity of the H+ + D and D+ + H dissociation thresholds: Feshbach resonances and the role of g/u-symmetry breaking

We report on the measurement and analysis of photoionisation, mass-analysed-threshold-ionisation and pulsed-field-ionisation zero-kinetic-energy photoelectron spectra of HD in the vicinity of the dissociative-ionisation thresholds H + D(1s) + e and H(1s) + D + e. The spectra were recorded via the vibrational levels of the and outer wells of the H and B states and provide information on the weakly bound levels of the X ground state of HD with vibrational quantum numbers and rotational angular-momentum quantum numbers . The spectra also reveal for the first time shape and Feshbach resonances of HD located energetically above the H + D(1s) dissociation limit. The structure and dissociation dynamics of the and states of HD and of the X and A states of HD near the dissociation thresholds are strongly influenced by the g/u-symmetry breaking caused by the nuclear-mass asymmetry.

Rotational Modulation of Ã2A″-State Photodissociation of HCO via Renner-Teller Nonadiabatic Transitions.

By examining the product-state distribution of a prototypical nonadiabatic predissociation system, HCO(Ã2A″-X̃2A'), we demonstrate that the dissociation dynamics is strongly modulated by parent rotational quantum numbers. The predissociation of the nominal (νC-H = 0, νbend, νC-O = 1) vibronic levels of the Ã2A″ state surprisingly gives rise to both vibrational ground and excited states of the CO product, despite the assumed spectator nature of the CO moiety. This anomaly is attributed to the dependence of the lifetime of the vibronic resonance facilitated by the Renner-Teller interaction on the parent rotational angular momentum quantum numbers coupled with transient intensity borrowing from nearby vibronic resonances with νC-O = 0. This unique phenomenon is a purely quantum mechanical behavior that has no classical analogue.

Spectroscopic parameters and transition probabilities of several doublet and quartet states of sulfoxide cation

In this work, the potential energy curves of 11 doublet, 11 quartet, and 2 sextet states of a sulfoxide cation are reported and the transition dipole moments between them were calculated. The radiative lifetimes were on the order of 10–6 s for the A2Π, C2Π, b4Σ–, and 12Σ+ states, approximately 10–6 – 10–7 s for the 12Δ and B2Σ– states, and on the order of 10–7 s for the 22Σ+ state. The radiative lifetimes of these states were short, suggesting that the spontaneous emissions generated from them occurred readily. Many transitions are strong, including A2Π – X2Π, C2Π – X2Π, C2Π – A2Π, B2Σ– – X2Π, B2Σ– – A2Π, 12Δ – X2Π, 12Δ – A2Π, and b4Σ– – a4Π. In addition, the transitions from the the first well of the 12Σ+ state to the X2Π state, and from the first well of the 22Σ+ state to the X2Π, A2Π, and C2Π states, are also strong. These strong transitions were easy to measure through spectroscopy. The properties of the transitions between certain Ω states generating from the X2Π, A2Π, a4Π, and b4Σ– states were investigated, including several electric dipole–forbidden transitions. The A2Π1/2 – X2Π1/2, A2Π3/2 – X2Π1/2, b4Σ–3/2 – a4Π5/2, b4Σ–1/2 – a4Π1/2, and b4Σ–1/2 – a4Π3/2 transitions are strong. The radiative litimes of the A2Π1/2, A2Π3/2, a4Π–1/2, a4Π1/2, a4Π3/2, a4Π5/2, b4Σ–1/2, and b4Σ–3/2 states were calculated and the distributions of their radiative lifetime varying as rotational angular momentum quantum number J were studied. The radiative lifetimes of the a4Π1/2 and a4Π3/2 states are on the order of several ms; those of the a4Π5/2 state are approximately several–ten ms; while those of the a4Π–1/2 state are on the order of several s. The results calculated herein can provide some useful guidelines for further experimental and astronomical observations and theoretical studies.

Transition properties of the X3Σ–g, A′3Δu, A3Σ+u, B′′3Πu, B3Σ–u, and B′3Πg states of sulphur dimer

In this study, we calculated the properties of the transition between six lowest-lying triplet states (X3Σ–g, A′3Δu, A3Σ+u, B′′3Πu, B3Σ–u, and B′3Πg) of sulphur dimer. The calculations were made with the CASSCF method, followed by the valence icMRCI approach. It was found that the radiative lifetime of the B3Σ–u state is in the order of 10 ns. The Einstein A coefficients of certain vibronic emissions from the B3Σ–u – X3Σ–g system were large, and the radiative lifetimes of the B′Πg and B′′Πu states were found to be in the order of 1 and 10 µs, respectively. The B′3Πg – A′3Δu, B′3Πg – A3Σ+u, and B′′3Πu – X3Σ–g transitions were strong and could be measured by spectroscopy. In contrast, the B′3Πg – B′′3Πu and B′3Πg – B3Σ–u transitions were weak and therefore, difficult to be detected via spectroscopy. The distributions of the radiative lifetimes with varying rotational angular momentum quantum number were evaluated for some lower vibrational states of the B′′3Πu, B3Σ–u, and B′3Πg states. The spin–orbit coupling effect on the transition properties of the B′′Πu – X3Σ–g system was also studied. The radiative lifetimes of the B′′3Πu, 0+, B′′3Πu, 1, and B′′3Πu, 2 states were in the order of 10−6 – 10−7, 10−6 – 10−7, and 10−5 s, respectively. The transition properties reported in this study can be used to guide the detection of sulphur dimers in both laboratory experiments and astrophysical environments.

Vibronic emissions and radiative lifetimes for a3Σ+, b3Π, c3Σ+, d3Δ, and e 3Σ– states of silicon monoxide

In this study, the potential energy curves of the a3Σ+, b3Π, c3Σ+, d3Δ, and e3Σ– states of the silicon monoxide are calculated and the transition dipole moments between them are computed using the complete active space self–consistent field, which is followed by the valence internally contracted multireference configuration interaction approach. The Davidson correction, core–valence correlation and scalar relativistic corrections are considered. The extrapolation of the potential energies to the complete basis set limit is included. The band origins, Einstein A coefficients, and Franck–Condon factors of all vibronic emissions between these five states are calculated. The rotationless radiative lifetimes are approximately 10–1 to 10–4 s for the b3Π state, 10–2 to 10–4 s for the d3Δ state, and 10–3 to 10–4 s for the e3Σ– state. The radiative lifetime quickly becomes shorter as the vibrational level increases for the three states. The lifetime is of the order of 100 ns for all vibrational levels of the c3Σ+ state, indicating that the spontaneous vibronic emissions originating from this state occurs easily. Overall, the vibronic emissions of the b3Π – a3Σ+, d3Δ – b3Π, and e3Σ– – b3Π systems are weak, suggesting that they are difficult to measure through spectroscopy. The vibronic emissions of the c3Σ+ – a3Σ+ and c3Σ+ – b3Π systems are strong, indicating that they are easy to measure in a spectroscopy experiment. The radiative lifetime with the variation of rotational angular momentum quantum number is discussed briefly for υ ≤ 15 and J ≤ 30 of the b3Π, c3Σ+, d3Δ, and e3Σ– states. The results indicate that the radiative lifetime changes only over a small range for each triplet state. The transition properties calculated in this study can be used to explain why only a few experimental transition properties are currently available for these triplet states.

Rotational and rovibrational transitions in the a 1Δ2 and b 1Σ+0+ states of sulfur monoxide radical

ABSTRACTSulfur monoxide radical has widely been detected in outer space using ground-state spectroscopy. The a 1Δ2 and b 1Σ+0+ states of this radical have low excitation energies, and they possibly exist in outer space. In this work, the potential energy curves and dipole moment functions of the two states were evaluated using the complete active space self- consistent field method, followed by the valence internally contracted multireference configuration interaction approach. The transition line positions, oscillator strengths, band transition dipole matrix elements, Einstein A coefficients, and Franck–Condon factors of all transitions were calculated for lower vibrational levels at rotational angular momentum quantum number J up to 150. The transition line positions calculated in this study are in good agreement with the experimental results. The rovibrational transition became noticeably weak at Δυ > 5. Comparing the results of a 1Δ2 and b 1Σ+0+ states reported in this paper with the previous values, we conclude that these results are the most accurate and complete to date.

Very high resolution far infrared synchrotron radiation spectrum of methanol-D1 (CH2DOH) in the first three torsional-vibrational modes

In our effort to systematically study the far infrared (FIR) spectra of asymmetrically mono deuterated methanol (CH2DOH) and thereby obtain the transition wavenumbers with better and better accuracy (Mukhopadhyay, 2016a,b), the complete Fourier transform (FT) spectra from FIR to infrared (IR) vibrational bands (in the range 50–1190cm−1) have been re-recorded using the Synchrotron Radiation Source at the Canadian Light Sources in Saskatchewan, Canada. The resolution of the spectrum is unprecedented, reaching beyond the Doppler limited resolution as low as about 0.0008cm−1 with a signal to noise (S/N) ratio is many fold better than that can be obtained by commercially available FT spectrometer using thermal sources (e.g., Globar). Spectra were also recorded beyond 1190cm−1 to about 5000cm−1 at a somewhat lower resolution of 0.002–0.004cm−1. In this report the analysis of the b-type and c-type torsional - rotational spectra in the ground vibrational state corresponding to gauche- (e1/o1) to gauche- (e1/o1) and gauche- (e1/o1) to trans- (e0) states in the ground vibrational state are reported and an atlas of the wavenumber for about 2500 FIR assigned absorption lines has been prepared. The transitions within a given sub-band are analyzed using state dependent expansion parameters and the Q-branch origins. The data from previous results (Mukhopadhyay, 2016a,b) along with the present work allowed a global analysis yielding a complete set of molecular parameters. The state dependent molecular parameters reproduce the experimental wavenumbers within experimental uncertainty. In addition, the sensitivity of the spectrum allowed observation of forbidden transitions previously unobserved and helped reassignment of rotational angular momentum quantum numbers of some ΔK=±1, Q-branch transitions in highly excited states recently reported in the literature. To our knowledge the wavenumbers reported in the present work are the most accurate so far reported in the literature and represent the highest resolution spectra for this molecular species.

Improved measurements and analysis of the far-infrared spectrum of methanol-D1 (CH2DOH) arising from trans- (e0) to gauche- (e1 & o1) states

In this work the millimeter-wave (MMW) and far infrared (FIR) absorption spectrum for the asymmetrically deuterated Methanol (CH2DOH) species measured recently at a temperature of −60°C with better accuracy and signal/noise (S/N) ratio than known before has been assigned for transitions originating at the lowest lying trans- to gauche-states. The entire spectrum for 50–1200cm−1 has been re-recorded recently using the Synchrotron Radiation Source coupled with the Bruker Fourier Transform Infrared (FTIR) spectrometer with a resolution of about 0.001cm−1 or better. Complete spectrum has not been exploited a great deal but it helped to entangle overlapping lines in the present work. This also fills the gap remaining in the usual FTIR in the range 400–500cm−1. Hence it is expected to help the interacting partner for the Coriolis interaction encountered earlier. The assigned transitions mostly for the axial rotational angular momentum quantum number K+1←K, both for R- and Q-sub bands for wide range of rotational angular momentum quantum number. The MMW spectrum has been recalibrated and assigned for a number of Q-branches. The assignments are confirmed rigorously using closed loop residual technique. The assigned rR and rQ lines have been analyzed in terms of polynomial expansion parameters. The new assignments are presented for about 750 transitions and a grand atlas of more than 1000 lines has been prepared which will be made available through the open source server at “research gate”. The present work should be useful in the area of astrophysical detection and further understanding of the energy relaxation pathways in the molecule.

Vibration–rotation spectroscopic database on acetylene, X˜1Σg+ (12C2H2)

A complete set of calculated vibration–rotation energies of 12C2H2 (X˜1Σg+) is provided for all vibrational states up to 13 000 cm−1 and some at higher energies, with rotational (J) and vibrational angular momentum (l) quantum numbers such that 0 ≤ J ≤ 100 and 0 ≤ |l| ≤ 20, respectively. The calculation is performed using a global effective Hamiltonian and related spectroscopic constants from the literature [B. Amyay et al., J. Mol. Spectrosc. 267, 80 (2011)], based on the polyad model. The numerical values of all related polyad matrix elements are also provided. The model and equations for the Hamiltonian matrix elements are gathered. The experimental acetylene database used for determining the parameters is listed.

New measurements and analysis of the far-infrared spectrum of CH2DOH in the lowest torsional vibrational state (e0)

In this work the far infrared (FIR) absorption spectrum has been measured for the asymmetrically mono deuterated Methanol (CH2DOH) species in the wavenumber range of 15–1200cm−1 better accuracy and signal/noise ratio than known before. Assignments have been made for b-type transitions in the lowest lying torsional vibrational state trans-(e0) for a wide range of rotational angular momentum. The assignments have been rigorously confirmed by the residual loop defect methods. The rR–branch wavenumbers are analyzed by the usual state dependent expansion parameters and the Q-Branch origins. These origins have been used to calculate the torsional and torsional-rotation interaction contributions. These findings are in good agreement with predicted from the Hamiltonian model described in recent publications. A large number of assignments have also been made in the millimeter wave spectrum recorded earlier and thereby evaluated the asymmetry splitting parameters for 4 different axial rotational angular momentum quantum numbers. The analysis and interpretation of the spectra are reported. New assignments for about 260 transitions are included the text and a catalog of about 1500 transitions belonging to the e0 species is prepared (Appendix 1) and is made available through the open server in “Research Gate” and will be freely available to others.

State-to-state resolved differential cross sections for rotationally inelastic scattering of ND3with He

State-to-state differential cross sections are reported for rotationally inelastic scattering of fully state-selected ND3 (j(k)(±) = 1(1)(-)) with He. Experimental measurements are compared with full close-coupling quantum-mechanical scattering calculations that used an ab initio potential energy surface. Results are presented for final states up to j'(k')(±) = 7(7)(-) at a mean collision energy of 430 cm(-1). For selected final quantum states, the effect of collision energy on the differential cross sections is also explored in the range 230-720 cm(-1). For the experimental studies, a hexapole electrostatic lens was used for the j(k)(±) state-selection of ND3 molecules in their electronic and vibrational ground states in a molecular beam. This state-selected molecular beam was then crossed with a beam of He atoms. The velocities of inelastically scattered ND3 molecules in single j'(k')(±) states were obtained by velocity map imaging, and converted to differential cross sections in the centre-of-mass frame by density-to-flux transformation. The close-coupling calculations reproduce well the measured angular distributions. For small changes in the rotational angular momentum quantum number (j), the ND3 is predominantly forward scattered, but the scattering shifts to the sideways and backward directions as Δj increases. For scattering into a given j'(k')(±) state, cross-sections for collisions that conserve the ± symmetry associated with the ND3 inversion vibration are larger and generally more forward scattered than the corresponding symmetry-changing processes.

Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculations

Rotationally inelastic scattering of methyl radicals (CD3 and CH3) in collisions with helium is examined by a combination of velocity map imaging experiments and quantum scattering calculations. In the experiments a beam of methyl radicals seeded in Ar intersects a beam of He atoms at 90° at a collision energy of 440 ± 35 cm−1 (CD3 + He) or 425 ± 35 cm−1 (CH3 + He). The methyl radicals are prepared photolytically in a gas expansion that cools them to 15 K, giving a distribution over a small number of initial (low) rotational angular momentum states. By resonance-enhanced multi-photon ionization detection, we obtain velocity map images which are specific to a single rotational angular momentum quantum number n′ of the methyl radicals, but averaged over a small subset of the projection quantum number k′. We extract resolved angular scattering distributions for n′ = 2–9 (for CD3). We compare these to predictions of scattering calculations performed based on a recent potential energy surface [P. J. Dagdigian and M. H. Alexander, J. Chem. Phys. 2011, 135, 064306] in which the methyl radical was fixed at its equilibrium geometry. The fully (n, k) → (n′, k′) resolved differential cross sections obtained from the calculations, when combined in weighted sums over initial (n, k) levels corresponding to the 15 K experimental radical temperature, and final k′ levels that are not resolved in the spectroscopic detection scheme, show excellent agreement with the experimental measurements for all final states probed. This agreement gives confidence in the calculated dependence of the scattering on changes in both the n and k quantum numbers.

The D1Πu state of HD and the mass scaling relation of its predissociation widths

Absorption spectra of HD have been recorded in the wavelength range of 75–90 nm at 100 K using the vacuum ultraviolet Fourier transform spectrometer at the Synchrotron SOLEIL. The present wavelength resolution represents an order of magnitude improvement over that of previous studies. We present a detailed study of the D1Πu–X1Σ+g system observed up to v′ = 18. The Q-branch transition probing levels of Π− symmetry are observed as narrow resonances limited by the Doppler width at 100 K. Line positions for these transitions are determined to an estimated absolute accuracy of 0.06 cm−1. Predissociation line widths of Π+ levels are extracted from the absorption spectra. A comparison with the recent results on a study of the D1Πu state in H2 and D2 reveals that the predissociation widths scale as μ−2J(J + 1), with μ being the reduced mass of the molecule and J the rotational angular momentum quantum number, as expected from an interaction with the B′1Σ+u continuum causing the predissociation.

Rotating full- and reduced-dimensional quantum chemical models of molecules

A flexible protocol, applicable to semirigid as well as floppy polyatomic systems, is developed for the variational solution of the rotational-vibrational Schrödinger equation. The kinetic energy operator is expressed in terms of curvilinear coordinates, describing the internal motion, and rotational coordinates, characterizing the orientation of the frame fixed to the nonrigid body. Although the analytic form of the kinetic energy operator might be very complex, it does not need to be known a priori within this scheme as it is constructed automatically and numerically whenever needed. The internal coordinates can be chosen to best represent the system of interest and the body-fixed frame is not restricted to an embedding defined with respect to a single reference geometry. The features of the technique mentioned make it especially well suited to treat large-amplitude nuclear motions. Reduced-dimensional rovibrational models can be defined straightforwardly by introducing constraints on the generalized coordinates. In order to demonstrate the flexibility of the protocol and the associated computer code, the inversion-tunneling of the ammonia ((14)NH(3)) molecule is studied using one, two, three, four, and six active vibrational degrees of freedom, within both vibrational and rovibrational variational computations. For example, the one-dimensional inversion-tunneling model of ammonia is considered also for nonzero rotational angular momenta. It turns out to be difficult to significantly improve upon this simple model. Rotational-vibrational energy levels are presented for rotational angular momentum quantum numbers J = 0, 1, 2, 3, and 4.

On the theory of complex-forming chemical reactions: effect of parity conservation on the polarization of differential cross sections

For complex-forming triatomic reactions such as the prototypical insertion reactions intensively studied in the last few years, quantum mechanical differential cross sections (DCS) present sharp forward/backward polarization peaks when the reagent rotational angular momentum quantum number j is zero. Moreover, the size of the peaks decreases rapidly with increasing j values so that for j = 3, they are no longer visible. In contrast, the polarization peaks are always missing in the classical mechanical DCSs. Apart from the peaks, however, the quantum and classical DCSs are usually in good agreement. In a recent rapid communication, we showed that the fundamental reason for the previous differences in the quantum and classical scenarios is that parity conservation leads in quantum mechanics to an angular momentum constraint without equivalent in classical mechanics. We also proposed a parity-restoring approximation leading to an accurate semi-classical description of the peaks. While only the main lines of the demonstration were given in the communication, we report here the whole developments. We also analyse why the peaks disappear when the reagent diatom is rotationally excited. As a by-product of the previous developments, we finally discuss the possibility of a general statistico-dynamical semiclassical approach.

State-resolved collisional quenching of vibrationally excited pyrazine (Evib=37900cm−1) by D35Cl(v=)

Supercollision relaxation of highly vibrationally excited pyrazine (E(vib) = 37,900 cm(-1)) with D35Cl is investigated using high-resolution transient IR diode laser absorption spectroscopy at 4.4 microm. Highly excited pyrazine is prepared by pulsed UV excitation at 266 nm, followed by rapid radiationless decay to the ground electronic state. The rotational energy distribution of the scattered DCl (v = 0,J) molecules with J = 15-21 is characterized by T(rot) = 755+/-90 K. The relative translational energy increases as a function of rotational quantum number for DCl with T(rel) = 710+/-190 K for J = 15 and T(rel) = 1270+/-240 K for J = 21. The average change in recoil velocity correlates with the change in rotational angular momentum quantum number and highlights the role of angular momentum in energy gain partitioning. The integrated energy-transfer rate for appearance of DCl (v = 0,J = 15-21) is k(2)(int) = 7.1x10(-11) cm3 molecule(-1) s(-1), approximately one-eighth the Lennard-Jones collision rate. The results are compared to earlier energy gain measurements of CO2 and H2O.

Microwave and ab initio studies of rare gas-methane van der Waals complexes.

Rotational spectra of the weakly bound Kr-methane van der Waals complex were recorded using a pulsed molecular beam Fourier transform microwave spectrometer in the range from 3.5 to 18 GHz. Spectra of 25 isotopomers of Kr-methane were assigned and analyzed. For isotopomers containing CH4, 13CH4, and CD4, two sets of transitions with K = 0 and one with K = 1 were recorded, correlating to the j = 0, 1, and 2 rotational levels of free methane, respectively (j is the rotational angular momentum quantum number of the methane monomer). For isotopomers containing CH3D and CHD3, two K = 0 components were recorded, correlating to the j(k) = 0(0) and 1(1) rotational levels of free methane (k corresponds to the projection of j onto the C3 axis of CH3D and CHD3). The obtained spectroscopic results were used to derive van der Waals bond distance R, van der Waals stretching frequency nu(s), and the corresponding stretching force constant k(s). Nuclear spin statistical weights of individual states were obtained from molecular symmetry group analyses and were compared with the observed relative transition intensities. The tentatively assigned j = 2 transitions were more intense than predicted from symmetry considerations. This is attributed to a relatively large effective dipole moment of this state, supported by ab initio dipole moment calculations. Ab initio potential energy calculations of Kr-CH4 and Ar-CH4 were done at the coupled cluster level of theory, with single and double excitations and perturbative inclusion of triple excitations, using the aug-cc-pVTZ basis set supplemented with bond functions. The theoretical results show that the angular dynamics of the dimer does not change significantly when the binding partner of methane changes from Ar to Kr. The dipole moment of Ar-CH4 was calculated at various configurations, providing a qualitative explanation for the unsuccessful spectral searches for rotational transitions of Ar-CH4.

High-Resolution Fourier Transform Spectrum of D2O in the Region Near 0.97 μm

The high-resolution Fourier transform spectrum of the D2O molecule were recorded and analyzed in the region near 0.97 μm (10 200–10 440 cm−1) where the bands of the v=4 (v=v1+v2/2+v3) polyad are located. Transitions belonging to the strongest band of the polyad, 3ν1+ν3, are assigned up to the value of the rotational angular momentum quantum number J=13. The presence of strong local resonance interactions allowed us to assign some transitions to the very weak band 4ν1. Upper states energies obtained on that basis were fitted with a Hamiltonian model which took into account resonance interactions between the states of the v=4 polyad. The derived spectroscopic parameters reproduce the overwhelming majority of assigned transitions within experimental accuracy.

High resolution laser spectroscopy beyond 18 eV: the [formula omitted] photoelectronic transition of N 2

Coherent, narrow-bandwidth laser radiation has been generated beyond 18 eV. The radiation has been used to record a rotationally resolved pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of the B 2Σ u +← X 1Σ g + transition of N 2. Analysis of the rotational structure indicates that the removal of one of the two 2σ u ∗ inner-valence-shell electrons is accompanied by substantial changes in the core rotational angular momentum quantum number: Rotational branches are observed with Δ N= N +− N=±1 and ±3, where N + and N represent the core rotational angular momentum of the ion and the neutral, respectively. These branches can be explained by the ejection of a photoelectron with dominant l=0 and l=2 character.

Isotope and temperature effects on nuclear magnetic shieldings and spin-rotation constants calculated at the coupled-cluster level

The temperature dependence of nuclear shieldings as well as isotope effects on shieldings and spin-rotation constants have been computationally investigated for H2, HF, F2, CO, and N2 employing the coupled-cluster singles and doubles (CCSD) method augmented by a perturbative treatment of triple excitations (CCSD(T)) for the calculation of potential curves, shieldings and spin–rotation functions together with finite-element techniques for the solution of the rovibrational problem. Calculated and measured temperature dependence of the isotropic shieldings agrees for N2, while for CO and F2 the computed temperature dependence is smaller than the experimental result. Isotropic shieldings have been deduced on the basis of our calculations from the measured spin-rotation constants for four isotopomers of H2 and agree, as required by theory. However, calculated and measured temperature dependence of the isotope shifts between HD and D2 differ by up to 10% which is larger than the estimated error bars for the experimental values. For HF and CO, calculated and measured isotope shifts agree, while for N2 no experimental data for comparison are available. In case of spin–rotation constants, the calculated dependence on the rotational angular momentum quantum number are for both H2 and F2 in good agreement with the dependence deduced from measurements, while for HF not enough experimental data are available for a comparison.